Sorry!. The problem is that Boolean is still try to treat this as a volume operation, which means that it may have contributions from both operands in the result. Now it is clear what parts of the planar thing are inside and outside the cutter box, but it is not clear what parts of the cutter box are “inside” and “outside” the planar thing (when regarded as a volume).
I think I eventually will add more modes to Boolean (more than just Union, Difference, Intersection). A mode that would help use cases like this would be a “Trim inside” mode, where the second operand still has to be closed (like your box) but the result of the operation would be defined as “only those parts of the first operand that are not inside the cutter”. There would also be a “Trim outside” mode. Other modes people have asked for would be ones like the “Knife Boolean” modes in the edit boolean tool – doing the face intersections but then doing different things with how those edges separate or do not separate the various pieces involved.